Clustering discretization methods for generation of material performance databases in machine learning and design optimization

Hengyang Li, Orion L. Kafka, Jiaying Gao, Cheng Yu, Yinghao Nie, Lei Zhang, Mahsa Tajdari, Shan Tang, Xu Guo, Gang Li, Shaoqiang Tang, Gengdong Cheng, Wing Kam Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


Mechanical science and engineering can use machine learning. However, data sets have remained relatively scarce; fortunately, known governing equations can supplement these data. This paper summarizes and generalizes three reduced order methods: self-consistent clustering analysis, virtual clustering analysis, and FEM-clustering analysis. These approaches have two-stage structures: unsupervised learning facilitates model complexity reduction and mechanistic equations provide predictions. These predictions define databases appropriate for training neural networks. The feed forward neural network solves forward problems, e.g., replacing constitutive laws or homogenization routines. The convolutional neural network solves inverse problems or is a classifier, e.g., extracting boundary conditions or determining if damage occurs. We will explain how these networks are applied, then provide a practical exercise: topology optimization of a structure (a) with non-linear elastic material behavior and (b) under a microstructural damage constraint. This results in microstructure-sensitive designs with computational effort only slightly more than for a conventional linear elastic analysis.

Original languageEnglish (US)
Pages (from-to)281-305
Number of pages25
JournalComputational Mechanics
Issue number2
StatePublished - Aug 15 2019


  • Heterogeneous materials
  • Machine learning
  • Materials database
  • Multiscale design optimization
  • Reduced order modeling

ASJC Scopus subject areas

  • Computational Mechanics
  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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